A brake caliper structure of the straddle seat off-road vehicle of the type concerned is disclosed, for example, in Japanese Utility Model Publication (JP-UM-B) No. 01-21096. The disclosed caliper structure includes a brake caliper movably connected to a pair of arms of a bracket bolted to support arms of a knuckle so that the arms extend astride an outer circumference of a brake disc. The brake caliper has two caliper pins extending parallel to an axis of rotation of the brake disc and slidably received via elastic bushings in holes formed in the respective arms of the bracket. Thus, the caliper is slidably mounted on the bracket.
With this arrangement, when a wheel rotatably mounted on the knuckle tilts in or out due to a force applied from a lateral direction thereof, the brake disc is tilted as it is integrally mounted on a hub of the wheel. In this instance, a tilt of the brake disc can be taken up or accommodated by the brake caliper because the brake caliper is elastically supported by the elastic bushings to the brackets. However, since the elastic bushings allow the brake caliper to tilt to a greater extent relative to the bracket, a care should be taken to insure smooth movement of the brake caliper relative to the bracket.